Kernel Knockoffs Selection for Nonparametric Additive Models

TL;DR

This paper introduces a kernel knockoffs method for nonparametric additive models that guarantees false discovery rate control at any sample size and improves variable selection power.

Contribution

It develops a novel kernel knockoffs procedure integrating subsampling and random feature mapping, ensuring FDR control for nonparametric models regardless of sample size.

Findings

FDR is controlled for any sample size

Method achieves high power as sample size increases

Outperforms existing variable selection methods in simulations

Abstract

Thanks to its fine balance between model flexibility and interpretability, the nonparametric additive model has been widely used, and variable selection for this type of model has been frequently studied. However, none of the existing solutions can control the false discovery rate (FDR) unless the sample size tends to infinity. The knockoff framework is a recent proposal that can address this issue, but few knockoff solutions are directly applicable to nonparametric models. In this article, we propose a novel kernel knockoffs selection procedure for the nonparametric additive model. We integrate three key components: the knockoffs, the subsampling for stability, and the random feature mapping for nonparametric function approximation. We show that the proposed method is guaranteed to control the FDR for any sample size, and achieves a power that approaches one as the sample size tends to infinity. We demonstrate the efficacy of our method through intensive simulations and comparisons with the alternative solutions. Our proposal thus makes useful contributions to the methodology of nonparametric variable selection, FDR-based inference, as well as knockoffs.